$89$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $106$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Explanation: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 89}$ ${x = 4y-106}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-106}$ for $x$ in the first equation. ${(4y-106)}{+ y = 89}$ Simplify and solve for $y$ $ 4y-106 + y = 89 $ $ 5y-106 = 89 $ $ 5y = 195 $ $ y = \dfrac{195}{5} $ ${y = 39}$ Now that you know ${y = 39}$ , plug it back into ${x = 4y-106}$ to find $x$ ${x = 4}{(39)}{ - 106}$ $x = 156 - 106$ ${x = 50}$ You can also plug ${y = 39}$ into ${x+y = 89}$ and get the same answer for $x$ ${x + }{(39)}{= 89}$ ${x = 50}$ There were $50$ home team fans and $39$ away team fans.